Question

Using molecular orbital theory, explain why the removal of one electron in \(\mathrm{O}_{2}\) strengthens bonding, while the removal of one electron in \(\mathrm{N}_{2}\) weakens bonding.

Short answer

When one electron is removed from O₂, it comes from a π*(2p) antibonding orbital, which results in strengthened overall bonding. In contrast, when one electron is removed from N₂, it comes from a π(2p) bonding orbital, leading to weakened overall bonding. This difference is explained by the molecular orbital theory and the energy diagrams of the molecular orbitals formed from the combination of atomic orbitals in both O₂ and N₂ molecules.

Step-by-step solution

Determine the Atomic Orbitals

For this exercise, we will focus on the valence electrons, since they're the ones involved in bonding. For both O₂ and N₂, we will look at the 2s and 2p atomic orbitals.

Form Molecular Orbitals

Using molecular orbital theory, atomic orbitals can form molecular orbitals through linear combinations. For diatomic molecules, the resulting molecular orbitals are either bonding or antibonding. We will focus on the sigma and pi orbitals formed by the combination of the 2s and 2p atomic orbitals.

Arrange Molecular Orbitals in Energy Diagrams

Next, arrange the molecular orbitals formed in Step 2 in the energy diagrams. For O₂ and N₂ molecules, the energy order of molecular orbitals is: 1. σ(2s) 2. σ*(2s) 3. σ(2p) 4. π(2p) = π(2p) 5. π*(2p) = π*(2p) 6. σ*(2p) The star (*) denotes an antibonding orbital.

Fill in Electrons in Molecular Orbitals

Oxygen has 6 valence electrons, giving O₂ a total of 12 valence electrons, while nitrogen has 5 valence electrons, giving N₂ a total of 10 valence electrons. Fill in the electrons in molecular orbitals, starting from the lowest energy orbital, taking into account Hund's rule and the Pauli exclusion principle. For O₂: 1. σ(2s) - 2e⁻ 2. σ*(2s) - 2e⁻ 3. σ(2p) - 2e⁻ 4. π(2p) = π(2p) - 4e⁻ (2 in each π orbital) 5. π*(2p) = π*(2p) - 2e⁻ (1 in each π* orbital) For N₂: 1. σ(2s) - 2e⁻ 2. σ*(2s) - 2e⁻ 3. σ(2p) - 2e⁻ 4. π(2p) = π(2p) - 4e⁻ (2 in each π orbital)

Analyze the Effect of Removing an Electron

Now, let's analyze the effect of removing one electron from each molecule. For O₂: When you remove one electron, it comes from one of the π*(2p) antibonding orbitals. With one electron less in an antibonding orbital, the overall bonding in O₂ is strengthened. For N₂: When you remove one electron, it comes from one of the π(2p) bonding orbitals. With one electron less in a bonding orbital, the overall bonding in N₂ is weakened.

Conclusion

Using molecular orbital theory, we can explain the different effects of removing one electron from O₂ and N₂. In O₂, electron removal strengthens bonding as it removes an electron from an antibonding orbital. In N₂, electron removal weakens bonding because it removes an electron from a bonding orbital.

Key concepts

Bonding in Diatomic Molecules

Understanding the nature of the bond between atoms in diatomic molecules is crucial for grasping how these entities hold together. The Molecular Orbital (MO) Theory offers a clear picture of how electrons are shared and organized between the two atoms. In MO Theory, individual atomic orbitals (AO) of the atoms in the molecule mix to form molecular orbitals, which extend over both atoms and can thus house the shared electrons of the bond.

These new orbitals come in two types: bonding molecular orbitals, which are lower in energy than the original atomic orbitals, and antibonding molecular orbitals, which are higher in energy. Electrons placed in bonding orbitals stabilize the molecule because they are in an energy state lower than they would be in separate atoms. In essence, for diatomic molecules like O₂ and N₂, electrons inhabiting bonding orbitals are the glue holding these molecules together.

Antibonding Orbitals

Antibonding orbitals play an intriguing, albeit less intuitive role in molecular stability. These orbitals, designated with an asterisk (e.g., σ* or π*), arise from the same AO interactions that create bonding orbitals, but they have a node between the nuclei where electron probability density is zero. Consequently, placing electrons in antibonding orbitals actually serves to increase the energy of the system, making the molecule less stable.

It's important to notice that the presence of electrons in antibonding orbitals does not always result in a molecular breakup. Molecules can and do exist with electrons in antibonding orbitals; the key is the balance between the number of electrons in bonding versus antibonding orbitals. For a stable molecule, there must be more electrons in bonding than in antibonding orbitals. This balance, known as bond order, helps us understand why removing an electron from an antibonding orbital in O₂ strengthens the bond, whereas removing one from a bonding orbital in N₂ weakens it.

Electronic Configuration of Diatomic Molecules

The electronic configuration of diatomic molecules is the arrangement of electrons in the molecular orbitals. According to MO theory, this configuration informs us about the bonding nature and stability of the molecule. To determine the electronic configuration, we follow a process similar to the Aufbau principle for atomic orbitals, with a focus on the energy levels specific to molecular orbitals.

In our exercise dealing with O₂ and N₂, the valence electrons from each atom are distributed across the resulting sigma (σ) and pi (π) orbitals. For O₂, with 12 valence electrons, the configuration ends up with two electrons in a high-energy antibonding orbital. For N₂, with 10 valence electrons, all electrons are paired in lower-energy bonding orbitals. This electron allocation in diatomic molecules is crucial to predict molecular properties like magnetism and reactivity, and to understand changes that occur when an electron is added or removed.